Explore BrainMass

Explore BrainMass

    Irreducible polynomial proof

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    Prove that X^n-1+X^n-2+........+X+1 is irreducible over Z iff n is prime.

    © BrainMass Inc. brainmass.com March 4, 2021, 7:32 pm ad1c9bdddf
    https://brainmass.com/math/basic-algebra/irreducible-polynomial-proof-107077

    Solution Preview

    Please see the attached file.

    Prove that is irreducible over Z iff n is prime.

    Proof:
    Let
    For n=2, we have f(x)=x+1, clearly is irreducible.
    Now we suppose n>2. Since n given as prime, n must be odd ...

    Solution Summary

    This provides an example of proving a polynomial is irreducible.

    $2.49

    ADVERTISEMENT